Hi there Gareth.
Generally, as a consumer journalist most of my working life, I'm pretty much automatically in favour of "us" against "them", particularly the big banks. However, in this case I'm sorry but I'm not clear exactly why you would expect a bank to "help" and how.
If you pay for something by cheque and it is cashed but you receive nothing, would you expect the bank to "help"?
If you went to a cash machine, withdrew £100 and bought 10 bottles of "perfume" from one of those nice men selling them out of a suitcase in the local High Street - and they turn out to be rancid rubbish, would you expect the bank to "help"?
What's so different about a debit card?
The credit card thing referred to by Barclays is specifically to do with the fact that if you paid for the goods by credit card (not debit or charge card), and the value is £100 or more, the credit card company has obligations to you, too, by virtue of S75 Consumer Credit Act 1974.
A principle known as equal liability means that both the credit card company and the supplier have the same obligations and responsibilities to you for the goods being satisfactory.
This, however, does not apply in respect of debit cards. Unfortunate but true.
As far as Purely Gadgets is concerned, I have just looked at its site. It appears to tick a number of key boxes in terms of its "accreditation" as a safe online dealer. It is highly unusual for a fake merchant to call you back if they are intent on ripping you off.
If you look in the r/hand corner of the site, you can see that the company is a member of ISIS, which has a click-through where you can raise a complaint if you are unhappy with the dealer. The company also publishes its address on the site, as well as an 0207 phone number. Again, unusual for a rip-off business.
This looks to me to be a case of poor service/***-up. I would suggest that you pursue your complaint through ISIS and the company. If things do not progress, you should contact the local trading standards department operating in the area, which looks to me to be Tower Hamlets. You might want to inform Purely Gadgets that you intend to do that.
In future, you might also want to confine your online purchases solely to a credit card.